ABSTRACT
In this chapter, the author discusses important properties of Poisson processes, the memoryless property and the Doeblin-Ito formula. The general counting processes are sometimes called renewal processes. One of the most important properties of the Poisson process is its memoryless property which is inherited by the exponential inter-times variables. The Poisson process can be interpreted as counting the number of clients arriving at exponential inter-arrival times. The Poisson thinning simulation technique allows the author to sample the jump times of a non-homogeneous Poisson process on any interval, as soon as the intensity is bounded by some homogeneous finite constant. The price to pay for this simplification is that the time to obtain a random sample from the non-homogeneous model can be very large.
